Hi, can someone please verify my answers to this question. Thanks heaps!!

Find all complex numbers w and z satisfying:

1/w + 1/z = 1/wz and 2wz - z^2 -1 = 0

- I got the answers z = 1/3 +(or)- (√2 / 3) i and w = 2/3 + (or) - (√2 / 3)i

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- Mar 11th 2013, 10:21 PMVishakComplex number algebra question
Hi, can someone please verify my answers to this question. Thanks heaps!!

Find all complex numbers w and z satisfying:

1/w + 1/z = 1/wz and 2wz - z^2 -1 = 0

- I got the answers z = 1/3 +(or)- (√2 / 3) i and w = 2/3 + (or) - (√2 / 3)i - Mar 11th 2013, 10:50 PMibduttRe: Complex number algebra question
You are absolutely right.

- Mar 12th 2013, 08:36 AMsmatikRe: Complex number algebra question
Yea correct.

- Mar 13th 2013, 02:41 AMalgerberRe: Complex number algebra question
Could someone please show me how you get this answer?

- Mar 13th 2013, 04:03 AMibduttRe: Complex number algebra question
- Mar 13th 2013, 08:52 AMHallsofIvyRe: Complex number algebra question
Multiply both sides of $\displaystyle \frac{1}{z}+ \frac{1}{w}= \frac{1}{wz}$ by wz to get w+ z= 1. Then w= 1- z so the second equation becomes $\displaystyle 2wz - z^2 -1= 2(1- z)z- z^2- 1= 2z- 2z^2- z^2- 1= -3z^2+ 2z- 1 = 0$ which the same as $\displaystyle 3z^2- 2z+ 1= 0$. Use the quadratic formula, or complete the square, to solve that for z